index.html (Mathematica 5.2 for Students - Personal Use Only)

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Laplace transform of an SD pulse with no tail

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[Graphics:HTMLFiles/index_5.gif]

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1/s - ^(-s)/s

change s to jw

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b = 1/( w) - ^(- w)/( w)

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-/w + ( ^(- w))/w

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[Graphics:HTMLFiles/index_12.gif]

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1/(^6 (-10000000 + s)) - ^(-3 s/5000000)/(-10000000 + s)

Replace s with jw

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d = 1/(^6 (-10000000 +  w)) - ^(-3  w/5000000)/(-10000000 +  w)

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1/(^6 (-10000000 +  w)) - ^(-(3  w)/5000000)/(-10000000 +  w)

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1/(^6 (-10000000 +  w)) - ^(-(3  w)/5000000)/(-10000000 +  w)

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1/(^6 (-10000000 +  w)) - ^(-(3  w)/5000000)/(-10000000 +  w)

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$Plot[Abs[d], {w, -1 * 10^8, 1 * 10^8}, ImageSize→600]$

[Graphics:HTMLFiles/index_23.gif]

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$LogLinearPlot[20 * Log[Abs[d]]/Log[10], {w, 10^5, 1 * 10^9}, ImageSize→600]$

[Graphics:HTMLFiles/index_26.gif]

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$Plot[180/π * ArcTan[Im[d]/Re[d]], {w, 1, 1 * 10^7}, ImageSize→600]$

[Graphics:HTMLFiles/index_29.gif]

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Created by Mathematica (January 29, 2007)